A101713 Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 27 for n > 0.

0, 2, 6, 9, 39, 418, 448, 1736, 2244, 3130, 3812, 5344, 5658, 5680, 8409, 9096, 11292, 21060

Offset

1,2

Comments

Numbers n such that 40*10^n + 3 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

Numbers corresponding to terms <= 448 are certified primes.

a(19) > 2*10^5. - Robert Price, Jul 17 2015

References

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Table of n, a(n) for n=1..18.

Makoto Kamada, Prime numbers of the form 400...003.

Formula

a(n) = A101397(n+1) - 1.

Example

4003 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 300], PrimeQ[40*10^#+3]&] (* Robert Price, Jul 17 2015 *)

Prog

(PARI) a=43; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-27)
(PARI) for(n=0, 1500, if(isprime(40*10^n+3), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A101397.

Sequence in context: A332066 A082459 A129831 * A240761 A342317 A117541

Adjacent sequences: A101710 A101711 A101712 * A101714 A101715 A101716

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(17)-a(18) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved